An extreme assumption would be that annuity markets are so imperfect that, for practical purposes, we can assume that annuities cannot be purchased. This assumption would obviously vitiate the argument that the failure of the wealthy to annuitize their wealth proves that they are not Life Cyclers. However, in the absence of annuities the Life Cycle model has other implications. In particular, it implies that selfish Life Cycle consumers, even patient ones, will eventually begin running down their wealth as they age. Figure 4 shows that by age 80 or so the HSZ model implies that consumers should be dissaving at a fairly substantial pace (the simulations here follow HSZ’s assumptions about mortality rates, which they derived from actuarial data, with the modification that they assume that death occurs for certain at age 100 if it hasn’t happened yet). However, Figure 5 shows the actual average age profile of wealth across the four SCF surveys. Although wealth accumulation slows, or perhaps halts, around age 65, there is no noticeable decumulation of assets for consumers in the top percentile of the wealth distribution.
Of course, nothing in economics requires us to believe that the only purpose of saving is to finance one’s own future consumption; that is merely a hypothesis of the basic Life Cycle model. One natural idea is that the wealthy do not run down their assets because they want to leave bequests to their children. This thought leads to the next model.
“I would as soon leave my son a curse as the almighty dollar.” Andrew Carnegie.
The Dynastic Model
In the 1995 issue of the annual Forbes 400 count of the richest Americans, there are at least 11 households containing descendants of Pierre du Pont (died 1817). This might seem to be compelling evidence that at least some of the very rich have a powerful bequest motive. On the other hand, apparently no members of the 400 trace their wealth to Robert Morris, reputed to be the wealthiest man in America at the time of the Revolutionary War. And Andrew Carnegie gave away over 90 percent of his fortune before he died. Furthermore, the fact that large bequests to children do occur does not prove that provision of such bequests is the primary motivation for accumulation.